The Magnus Effect, what is the formula/equation?

[JordanKnowles]

I'm currently doing a project for my A-Level Physics group, and I have chosen to look into the Magnus Effect, however, I'm struggling to find an equation for it? Really need help here! Thank you!

 

[Simon Bridge]

Welcome to PF;
The Magnus effect is that the more difficult the physics the more the physicist waves his arms about when explaining it. Re:


... however you probably mean the effect where spinning generates a deflecting force.
http://farside.ph.utexas.edu/teaching/329/lectures/node43.html

 

[rcgldr]

I'm not aware of real world formulas. There are idealized formulas for spinning cylinders, but these are fairly off from actual real world examples.

Wiki article, the lift force related to Magnus effect is due to diversion of air flow in the wake that trails the spinning ball:

http://en.wikipedia.org/wiki/Magnus_effect

Another archived separation of flow explanation:

wayback_machine_magnus_effect.htm

 

[JordanKnowles]

Thank you! But with the equation f(magnus) = S(v)w x v
What does the S(v)w mean?
Also, in the farside article, what is the B=S/m equation for?

 

[Simon Bridge]

S will be the spin of the ball, which is a function of it's speed, w is actually $\omega$ - the angular velocity, and v is the linear velocity. The x in the middle is a cross product. So that's $S(v)[\vec{\omega} \times \vec{v}]$ ... you have to read some of htese things quite carefully since they will gve you the definitions by implication rather than explicitly.

There's quite a bit about the magnus force out there - you should read around.

 

[JordanKnowles]

Okay, thank you very much!

 

[sophiecentaur]

I'm not aware of real world formulas. There are idealized formulas for spinning cylinders, but these are fairly off from actual real world examples.

Wiki article, the lift force related to Magnus effect is due to diversion of air flow in the wake that trails the spinning ball:

http://en.wikipedia.org/wiki/Magnus_effect

Another archived separation of flow explanation:

wayback_machine_magnus_effect.htm

This has to be the underlying (correct) 'reason' because, otherwise one would have a reactionless force. How the air is deflected must also be for (correct) aerodynamic reasons. As with the concurrent discussion thread on How Aeroplanes Fly, people introduce a similar false dichotomy. Can't we maintain more than one ball in the air at a time (mentally)?